Strong coupling regime of cavity quantum electrodynamics and its consequences on molecules and materials

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Strong coupling regime of cavity quantum

electrodynamics and its consequences on molecules and

materials

Thibault Chervy

To cite this version:

Thibault Chervy. Strong coupling regime of cavity quantum electrodynamics and its consequences on molecules and materials. Theoretical and/or physical chemistry. Université de Strasbourg, 2017. English. �NNT : 2017STRAF033�. �tel-01715300�

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UNIVERSITÉ DE STRASBOURG

ÉCOLE DOCTORALE ED222

UMR 7006

THÈSE

présentée par :

Thibault CHERVY

soutenue le : 15 Septembre 2017

pour obtenir le grade de :

Docteur de l’université de Strasbourg

Discipline/ Spécialité

: Physique

Strong coupling regime of cavity quantum

electrodynamics and its consequences on

molecules and materials

Régime de couplage fort de l’électrodynamique

quantique en cavité et conséquences pour les

molécules et les matériaux

THÈSE dirigée par :

M. EBBESEN W. Thomas Prof. Dr., ISIS, Université de Strasbourg

RAPPORTEURS :

M. RUBIO Angel Prof. Dr., Max Planck institute for structure and dynamics of matter M. GOMEZ RIVAS Jaime Prof. Dr., Dutch institute for fundamental energy research

AUTRES MEMBRES DU JURY :

M. GENET Cyriaque Dr., ISIS, CNRS - Université de Strasbourg M. PUPILLO Guido Prof. Dr., IPCMS, Université de Strasbourg M. IMAMOGLU Ataç Prof. Dr., Institut für Quantenelektronik

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C O N T E N T S

1 l i g h t m a t t e r s t r o n g c o u p l i n g f o r n o v e l m a

-t e r i a l a n d c h e m i c a l p r o p e r -t i e s 8

1.1 A brief and partial historical perspective 9 1.2 Light-molecules strong coupling 12

1.2.1 Molecules for cQED? 12

1.2.2 The molecular strong coupling regime 17 1.2.3 A two-level systems approach: the

Jaynes-Cummings model 22

1.2.4 More complex models: toward cavity quan-tum chemistry 28

2 d y n a m i c s a n d e n e r g y f l o w i n s t r o n g ly c o u

-p l e d m o l e c u l e s 32

2.1 Fluorescence quantum yield and transient

dy-namics 33

2.1.1 Spatial tuning of strong coupling in FP cavities 33

2.1.1.1 Experimental methods 33 2.1.1.2 Results and discussion 35 2.1.2 PL quantum yield and transient

dynam-ics 40

2.1.2.1 Experimental methods 40 2.1.2.2 Results and discussion 41

2.1.2.3 Transient polariton dynamics 43 2.1.3 Conclusions 46

2.2 Polariton photophysics: a rich chemical diver-sity 47

2.2.1 Systems under study 47

2.2.2 Populating the lower polaritonic states 50

2.2.2.1 Fluorescence excitation spectroscopy 52 2.2.2.2 Results and discussion 53

2.2.3 Conclusions 55

2.3 Energy transfer through light-matter hybrid states 57

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c o n t e n t s iv

2.3.1 Energy transfer in a cascade coupling con-figuration 57

2.3.1.1 System under study 58 2.3.1.2 Hints of energy transfer in steady

state spectra 60

2.3.1.3 Time-resolved polaritonic energy transfer 63

2.3.2 Energy transfer between spatially sepa-rated entangled molecules 67

2.3.2.1 Static and transient signatures 67 2.3.2.2 Cavity Förster model of

polari-tonic energy transfer 70

2.3.3 Conclusions 78

2.4 Second harmonic generation from polaritonic states 78 2.4.1 Systems under study 79

2.4.2 SHG measurements 83 2.4.3 Conclusions 89

3 v i b r a t i o n a l l i g h t- m a t t e r s t r o n g c o u p l i n g 91 3.1 Multiple Rabi splittings under ultrastrong

vibra-tional coupling 92

3.1.1 System under study 93

3.1.2 Vibrational multimode coupling 94

3.1.3 Signatures of multimode vibrational USC 100 3.1.3.1 Collective vibrational coupling:

a model for ultra-strongly cou-pled oscillators 100

3.1.3.2 Results and discussion 107 3.1.4 Conclusions 111

3.2 Vibro-polaritonic IR emission in the strong cou-pling regime 112

3.2.1 System under study 112

3.2.2 FTIR emission spectroscopy of vibro-polaritons 115 3.2.3 Conclusions 119

4 c h i r a l l i g h t- c h i r a l m a t t e r s t r o n g c o u p l i n g 120 4.1 Strong coupling of WS₂ monolayers with

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c o n t e n t s 1

4.1.1 WS₂, a natural candiate for light-matter strong coupling 122

4.1.2 Light-matter strong coupling at the 2D limit 124

4.2 Spin-momentum locked polaritons under chiral strong coupling 133

4.2.1 System under study 137 4.2.2 Results and discussion 139 4.2.3 Methods 152 4.2.4 Conclusions 155 5 c o n c l u s i o n s a n d o u t l o o k s 156 6 r é s u m é d e l a t h è s e 158 6.1 Context 158 6.2 Résultats et discussions 160 6.3 Conclusion 166 b i b l i o g r a p h y 171

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L I S T O F P U B L I C AT I O N S

j o u r n a l p u b l i c a t i o n s

Work covered in this thesis

• T. Chervy, A. Thomas, E. Akiki, R. M. A. Vergauwe, A. Shalabney, J. George, E. Devaux, J. A. Hutchison, C. Genet and T. W. Ebbesen

Vibro-polaritonic IR emission in the strong coupling regime,

Submitted for publication

• T. Chervy?, S. Azzini?, E. Lorchat, S. Wang, Y. Gorodetski, J. A. Hutchison, S. Berciaud, T. W. Ebbesen and C. Genet, Spin-momentum locked polariton transport in the chi-ral strong coupling regime,

Submitted for publication

• X. Zhong, T. Chervy, L. Zhang, A. Thomas, J. George, C. Genet, J. A. Hutchison and T.W. Ebbesen,

Energy transfer between spatially separated entangled molecules,

Angew. Chem. Int. Ed. (2017)

• J. George?, T. Chervy?, A. Shalabney, E. Devaux, H. Hiura, C. Genet and T. W. Ebbesen,

Multiple Rabi splittings under ultra-strong vibrational coupling,

Phys. Rev. Lett., 117, 153601 (2016).

• T. Chervy, J. Xu, Y. Duan, C. Wang, L. Mager, M. Frerejean, J. A. W. Münninghoff, P. Tinnemans, J. A. Hutchison, C. Genet, A. E. Rowan, T. Rasing and T. W. Ebbesen,

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c o n t e n t s 3

High efficiency second-harmonic generation from hy-brid light-matter states,

Nano Lett., 16, 7352-7356 (2016)

• S. Wang?, S. Li?, T. Chervy?, A. Shalabney, S. Azzini, E. Orgiu, J. A. Hutchison, C. Genet, P. Samorì and T. W. Ebbesen,

Coherent coupling of WS2 monolayers with metallic

photonic nanostructures at room temperature, Nano Lett., 16, 4368-4374 (2016)

• X. Zhong, T. Chervy, S. Wang, J. George, A. Thomas, J. A. Hutchison, E. Devaux, C. Genet and T. W. Ebbesen,

Non-radiative energy transfer mediated by hybrid light-matter states,

Angew. Chem. Int. Ed., 55, 6202-6206 (2016)

• J. George, S. Wang, T. Chervy, A. Canaguier-Durand, G. Schaeffer, J.-M. Lehn, J. A. Hutchison, C. Genet and T. W. Ebbesen,

Ultra-strong coupling of molecular materials: spectroscopy and dynamics

Farad. Discuss., 178, 281-294 (2015)

• S. Wang, T. Chervy, J. George, J. A. Hutchison, C. Genet and T. W. Ebbesen

Quantum yield of polariton emission from hybrid light-matter states

J. Phys. Chem. Lett., 5, 1433-1439 (2014)

Other publications

• A. Thomas, J. George, A. Shalabney, M. Dryzhakov, S. J. Varma, J. Moran, T. Chervy, X. Zhong, E. Devaux, C. Genet, J. A. Hutchison and T. W. Ebbesen,

Ground-state chemical reactivity under vibrational cou-pling to the vacuum electromagnetic field,

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c o n t e n t s 4

• R. M. A. Vergauwe, J. George, T. Chervy, J. A. Hutchison, A. Shalabney, V. Torbeev and T. W. Ebbesen,

Quantum strong coupling with protein vibrational modes, J. Phys. Chem. Lett., 7, 4159-4164 (2016).

• Y. Gorodetski, T. Chervy, S. Wang, J. A. Hutchison, A. Drezet, C. Genet and T. W. Ebbesen,

Tracking surface plasmon pulses using ultrafast leakage imaging,

Optica, 3, 48-53, (2016)

c o n f e r e n c e p r e s e n t a t i o n s

• ACS on Campus, Strasbourg November 25, 2016 (Talk) Hybrid light-matter states: a molecular and material science perspective

T. Chervy

• NIE scientific day, Strasbourg June 14, 2016 (Poster)

Multiple Rabi splitttings under vibrational ultra-strong coupling

J. George?, T. Chervy?, A. Shalabney, E. Devaux, H. Hiura, C. Genet and T. W. Ebbesen

• GDR Ondes on Nonlinear and Quantum Plasmonics, Marseille June 2, 2016 (Talk)

Efficient second harmonic generation from hybrid light-matter states

T. Chervy, J. Xu, Y. Duan, C. Wang, L. Mager, M. Frerejean, J. A. W. Münninghoff, P. Tinnemans, J. A. Hutchison, C. Genet, A. E. Rowan, T. Rasing and T. W. Ebbesen

• ICSCE8 on Hybrid Polaritonics, Edinburgh April 25-29, 2016 (Poster)

Multiple Rabi splitttings under vibrational ultra-strong coupling

J. George?, T. Chervy?, A. Shalabney, E. Devaux, H. Hiura, C. Genet and T. W. Ebbesen

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c o n t e n t s 5

• International School of Physics ’Enrico Fermi’ on Complex photonics, Varenna July 18, 2015 (Talk)

Molecules in the strong coupling regime

J. George, S. Wang, T. Chervy, A. Canaguier-Durand, G. Schaeffer, J.-M. Lehn, J. A. Hutchison, C. Genet and T. W. Ebbesen

• Faraday discussion on Nanoplasmonics, London February 16-18, 2015 (Poster)

Ultra-strong coupling of molecular materials: spectroscopy and dynamics

J. George, S. Wang, T. Chervy, A. Canaguier-Durand, G. Schaeffer, J.-M. Lehn, J. A. Hutchison, C. Genet and T. W. Ebbesen

• ISIS Young Scientist Seminar, Strasbourg July 3, 2014 (Talk) The strong coupling of your light with my matters T. Chervy

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S Y N O P S I S

Since its early developments in cold atoms physics in the 1980s [1], the vacuum strong coupling regime of cavity quan-tum electrodynamics (cQED) has emerged as a new frontier of science by providing unprecedented control of matter by light and of light by matter [2]. Recent achievements in Bose-Einstein condensation [3–6], superfluidity [7–9], entanglement swap-ping [10], topological operations [11], synthetic gauge design [12,13] and modified chemical reactions [14, 15] among many others, hold great promises for future technological applica-tions of strongly coupled systems [16], and open new avenues of fundamental research [17].

This regime has been realized on a rich variety of plat-forms, embracing semiconductor quantum wells [18], super-conducting q-bits [19], nuclear X-ray transitions [20], as well as electronic [21] and vibrational [22] transitions of organic materials. Quite remarkably, such different realizations of light-matter strong coupling, ranging from the gigahertz to the hard X-ray energies, can all be understood on the basis of a very simple coupled oscillators Hamiltonian [23]. When the light-matter coupling strength becomes sufficiently high, this model predicts the appearance of new eigen-states, termed polaritonic states, sharing properties of both light and matter. The hybrid nature of such states provides a unique opportu-nity to intertwine the non-local and propagating behavior of light with the localized, interacting, and potentially nonlinear behavior of matter. Thus, despite their formal equivalence, the specificities of each platforms in terms of their coupling to an ’environment’ and their intrinsic non-linearities give rise to a wealth of different research directions.

In this thesis, we have investigated different aspects of light-matter strong coupling involving macroscopic ensembles

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c o n t e n t s 7

of molecules collectively coupled to a common cavity mode. The new chemical and material properties offered by those polaritonic states pave ways to the currently emerging field of Rabi chemistry. Our contribution to this work has been organized in four chapters.

• The first chapter aims at giving a broad overview of the vacuum strong coupling regime of cQED, starting with a brief historical perspective, and introducing some of the key concepts of strong light-molecules interaction. Several state of the art developments are exposed, giving a general context to this work.

• In the second chapter, we investigate the population dy-namics and energy pathways in strongly coupled molecu-lar systems. This chapter compiles different experimental approaches both in the static and transient regimes, and gives a glimpse at the broad range of possibilities offered by light-matter strong coupling in complex molecular landscapes.

• The third chapter is concerned with the strong coupling of optical resonances with molecular vibrations in the IR domain. This regime of vibrational strong coupling opens new horizons in the context of modified chemical reactions under light-matter interaction, and non-linear polariton dynamics.

• In chapter 4, we investigate the rich interplay between light-matter strong coupling and chirality. This is done by coupling chiral spin-orbit plasmonic modes at a metal surface with the valley contrasted excitons of a 2D transi-tion metal dichalcogenide monolayer. In this regime, we observe surprisingly robust material coherences, revealing the ability of polaritonic states to protect specific degrees of freedom from decoherence, a phenomenon underlying several other results presented in this thesis.

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L I G H T- M AT T E R S T R O N G C O U P L I N G F O R

N O V E L M AT E R I A L A N D C H E M I C A L P R O P E R T I E S

Light-matter interaction is a key process in modern tech-nologies, constituting a fast interface between propagating op-tical modes mediating information over long distances, and localized material states with potentially large nonlinearities. This interplay between weakly and strongly interacting systems allows for efficient switching, routing and computing, which are currently driving the research effort in a broad field ranging from material sciences to cold atoms and from telecom optics to nanophotonics. In quest of integrability, tailoring light-matter interaction at the (sub-)wavelength scales is thus leading to an emerging class of devices with unprecedented properties, where an effective photon-photon interaction is obtained from the nonlinearity of the material medium [24–28].

Light-matter interaction can however also be considered from a opposite perspective, where an effective nonlocality arises in the material due to its interaction with extended photonic modes. This approach is rooted in the pioneering work of Purcell on the modification of the relaxation rate of a spin in a RLC resonator in 1946 [29] and its later extension to the visible frequency domain by Drexhage in 1974 [30]. In those celebrated experiments, the light matter coupling frequency remained lower than the relaxation frequency of each systems toward the environment, such that only the spontaneous decay rate and the Lamb shift of the transition could be affected. This regime, later termed ‘weak coupling regime’, constitutes

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1.1 a brief and partial historical perspective 9

nevertheless the first demonstration of the modification of ma-terial properties by tailoring the surrounding electromagnetic vacuum. In other words, properties that were thought to be intrinsic to matter turned out to be properties of the matter dressed by its electromagnetic environment. The possibility of dressing material resonances to control and modify specific molecular properties is at the heart of this thesis work.

1.1 a b r i e f a n d pa r t i a l h i s t o r i c a l p e r s p e c t i v e

Even though remarkable effects of the surrounding electro-magnetic environment on the radiative properties of atoms and molecules could be observed by placing them near a metallic re-flector, the most dramatic modifications of their properties were expected to happen when the light-matter coupling strength would overcome any of the possible relaxation rates. To our knowledge, the first experimental demonstration of this strong coupling regime was reported in 1975 by Yakovlev, Nazin and Zhizhin [31], following the theoretical work of Agranovich and Malshukov [32]. In 1983, the first cold atoms experiment to reach this regime was reported by Kaluzny and coworkers, using a cloud of sodium Rydberg atoms in a superconducting Fabry-Pérot resonator [1].

In such cavity QED experiments, the spectral density J(ω), quantifying the interaction strength between the atoms and their surrounding electromagnetic vacuum states is dramati-cally modified by the field boundary conditions imposed by the cavity. The redistribution of this spectral density over sharp frequency ranges, i.e. cavity modes, can lead to situations where J(ω) is non-constant over an energy range of the order of J(ω)/ h, resulting in a light-matter coupling frequency higher than the memory time of the cavity mode [2, 33]. In this ringing regime of cQED, favored by coupling large ensembles of absorbers to high finesse cavities, the dynamical evolution of the absorber-field system is strikingly different from that observed under weak coupling. In particular, the irreversible

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1.1 a brief and partial historical perspective 10

spontaneous emission is replaced by a reversible exchange of energy between the field and the atoms, giving rise to periodic Rabi oscillations. Accordingly, the energy levels of the atoms and the field hybridize into two new polaritonic eigen-states which are coherent superpositions of light and matter, separated in energy by the inverse of the Rabi period TR, the Rabi splitting ΩR[23].

With Rabi splittings potentially reaching significant frac-tions of the energy of the coupled transifrac-tions, light-matter strong coupling must lead to a complete redefinition of the potential energy surfaces of the system, with profound impli-cations on its chemical and material properties. Moreover, provided that the N absorbers present in the cavity remain indistinguishable with respect to their coupling to the mode, they would participate collectively in the formation of the hybrid light-matter states [34]. This collective eigen-states splitting is one of the hallmarks of the light-matter strong coupling regime. It shows how an incoherent ensemble of distant absorbers can spontaneously cooperate in shared and delocalized hybrid states. We have here the two levers that will be used throughout this work: modified energetics and collectivity.

The observation of temporal Rabi oscillations and en-ergy levels splitting triggered a huge interest from a broad community of researchers, while the fundamental aspect of this phenomenon allowed different platforms to be explored, in particular using quantum wells in semiconductor micro-cavities [18]. While major efforts were devoted to reach the single atom strong coupling regime, with the aim of realizing highly nonlinear systems where, for instance, the state of a single atom could switch the transitivity of the whole system [35], the pioneering groups of semiconductor strong coupling [36] focused on the possibilities offered by polariton-polariton interactions inherent to many-body strong coupling.

After 25 years of active research, the field of semiconduc-tor strong coupling continues to progress with the demonstra-tion of polariton Bose-Einstein condensademonstra-tion [3–6],

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superfluid-1.1 a brief and partial historical perspective 11

ity [7–9], entanglement swapping [16], topological operations [11], or synthetic gauge design [12,13] among many others.

Unlike those very dynamical developments in inorganic semiconductors, the early demonstration of molecular strong coupling passed almost unnoticed, likely due to the typically small exciton radii in such systems (hence the weak polariton-polariton interactions) and the comparatively high material disorder. Room temperature exciton-surface plasmon strong coupling was indeed already reported in 1982 by Pockrand and coworkers [21] using Langmuir-Blodgett films of molec-ular self-assemblies. Fifteen years (and 14 citations) later, a theoretical proposal by Agranovich [37] and two experimental papers by Fujita et al. [38] and Lidzey et al. [39] renewed the interest in this field. With their small dielectric constants and high oscillator strengths organic semiconductors were shown to provide the large and robust Rabi splittings required for room temperature strong coupling, while their hybridization with Wannier-Mott inorganic excitons could offer new ways to engi-neer relaxation mechanisms. With the technical progresses in thin film deposition and cavity mirror coatings, it thus became apparent that organic strong coupling could play a key role as a low cost, easy to make, room temperature stable candidate to realize the fascinating phenomena observed with quantum well polaritons. This perspective has driven a considerable research effort over the last decade, eventually leading to the demonstration of room temperature polariton lasing [40–44] and superfluidity [45] in organic materials.

But beside their robust excitonic nature and relative ease of processability, strongly coupled molecular materials had something fundamentally new to offer: their chemical complex-ity and direct link to material sciences. This aspect of molecular strong coupling, completely overlooked at this time, is what motivated Ebbesen and coworkers to undertake research on this subject in 2003 [46], laying the ground for a new field at the interface of cQED and molecular and material sciences.

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1.2 light-molecules strong coupling 12

1.2 l i g h t- m o l e c u l e s s t r o n g c o u p l i n g

Rather than directly giving an Hamiltonian description of a generic strongly coupled system [47–49], we will here follow a more heuristic approach, and try to introduce some of the key concepts of molecular polariton physics as they reveal them-selves through experiments. The celebrated Jaynes-Cummings model of polariton physics [23] will then naturally arise as an extreme simplification of those systems. Recent extensions of this model toward an accurate description of strong coupling in complex molecular systems will be briefly reviewed.

1.2.1 Molecules for cQED?

Molecules, often displaying hundreds of ro-vibrational modes, flexible backbones, inherent disorder and notoriously interacting with their environment, are clearly not the first systems that come in mind when thinking about QED experi-ments. Despite this fact, several studies have shown that they can display a rich variety of quantum phenomena, directly related to the survival of electronic or vibrational coherences over picoseconds time scales. For instance, oscillatory dynamics in the transient absorption spectra of photosynthetic complexes was already reported in 1995 [50], raising fascinating questions on the role of quantum coherences in the function and reactivity of chemical and biological systems. The wealth of experiments that followed [51] opened the blossoming field of quantum biology, where coherences, entanglement and disorder partic-ipate in the efficiency of energy transport in pigment-protein complexes [52,53].

Another striking example where quantum effects emerge in molecular systems is found in supramolecular aggregates [54, 55]. In such systems, individual chromophores can self-assemble into supramolecular entities with excited states span-ning extended domains of coherently coupled monomeric units. As the molecular excitons are then delocalized over tens of

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Figure 1.1– Absorbance spectrum of a dilute monomeric solution of the amphiphilic cyanine dye TDBC in ethanol (cyan curve), and of its J-aggregated form obtained by the addition of a strong base (NaOH, orange curve).

monomers, their absorption and emission spectra dramatically change from a broad vibronic progression to a sharp and very intense line with essentially no vibrational substructure (see e.g. Fig.1.1). Such a disappearance of vibrational substructure, reminiscent of motional narrowing for solvated molecules, is here a direct manifestation of quantum delocalization where the exciton wavepacket sees an effective disorder averaged over its localization volume [56–58].

Besides the perspectives they offer in exploiting room temperature quantum coherences, molecular systems naturally lend themselves as good candidates for cQED experiments due to their potentially very large transition dipole moments (extinc-tion coefficients up to 106_M−1_cm−1_{), favoring their coupling to}

electromagnetic modes. As we will discuss in the next sections, this coupling can in some cases compare favorably to any other relaxation rates of the molecular excitons, setting the stage for light-molecule strong coupling.

A typical visible absorption spectrum of a solution of molecules at room temperature is shown in Fig.1.2(a). It results from a complex variety of electronic transitions from molecular

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ground states to different vibrationally hot excited states. Just after the rapid electronic transition, the new charge distribution is usually out of equilibrium with the surrounding medium and the molecular backbone, leading to an energy relaxation toward a new equilibrium configuration (Fig.1.2(b)). From this relaxed configuration, the molecule can decay back to the electronic ground state manifold via many different processes such as the emission of a photon, internal vibrational relaxation or inter-system crossing to a manifold of different spin multiplicity followed by phosphorescence.

The linewidth of absorption of a single molecule at T = 0K, assuming the absence of intramolecular vibrations, consists of a sharp and intense line corresponding to a purely electronic tran-sition (PEL), as sketched in Fig. 1.2(c), top-left. The linewidth Γ (0) of such a transition is only determined by the electronic state lifetime, and usually lies in the range of 10−4−10−3cm−1 for allowed optical transitions [59]. In condensed phase, this PEL is accompanied by a broad continuum corresponding to the coupling of the electronic excited state to the spectrum of acoustic phonons of the embedding matrix or solvent. As the temperature is raised, the thermal population of those phonons modes can (quasi-)elastically scatter off the excited electron, causing random phase jumps in its wavefunction. This purely dephasing mechanism thus effectively shortens the lifetime of the quantum coherent state, while leaving its population unchanged, and hence corresponds to a broadening of the PEL linewidth Γ with temperature:

Γ (T ) = 1 πcT2(T ) = 1 πc 1 2T1(T ) + 1 T₂∗(T ) , (1.1)

where T2 is the overall coherence time of the excited electronic

state, T1is the population lifetime, including radiative and

non-radiative decays, and T₂∗is the phase relaxation time. In addition to PEL broadening, increasing the temperature also transfers absorption strength from the PEL to its phonon side-bands, resulting in the absence of such purely electronic sharp line

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in the measured room temperature spectra, even for individual molecules, as sketched in Fig.1.2(c), top row. Moreover, owing to their backbone structure, molecules also have intramolec-ular vibrational modes, giving rise to vibronic zero-phonon lines where the electronic transition is accompanied by the excitation of a molecular vibration, without populating the phonon modes of the environment. These vibronic zero-phonon lines are also accompanied by their own phonon side-bands, as depicted in the middle row of Fig. 1.2(c), and their oscillator strength are determined by Franck-Condon factors, optical selection rules, and the symmetry and populations of the states involved. Finally, when measuring molecular ensembles, as in Fig.1.2(a), the dynamic local energetic disorder associated with the solvation of molecules shuffles these spectral features over a broad span of c.a. 100 − 1000cm−1. At room temperature, this inhomogeneous broadening usually dominates the spectral response of disordered molecular ensembles, as shown in the last row of Fig.1.2(c).

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Figure 1.2 – (a) Normalized absorption and emission spectra of Rhodamine B in an ethanol solution. The energy shift in fluorescence emission (Stokes shift) indicates the relaxation dynamics of the electronic wave-function in the excited and ground state manifolds following the optical transitions. (b) Schematic energy levels diagram of the optical cycle between the ground (n0) and excited (n1) electronic state

manifolds. The strength of the different vibronic optical transitions are dictated by the Franck-Condon overlaps, optical selection rules, the symmetry of the molecular orbitals and the occupancy of the states. (c) First row: schematic absorption spectrum of a solvated two-levels molecule. With increasing temperatures, the PEL linewidth Γ broadens and looses strength while the phonon side-band broadens and increases in intensity. Second row: schematic including additional vibronic transitions νiand their phonon side-bands.

Third row: ensemble averaging of the spectra in presence of (Gaussian) energetic disorder. The schematic illustrations are adapted from [59].

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Overall, these different factors result in broad, inhomo-geneous and complex line shapes for the room temperature molecular chromophores ensembles that we will study. This inhomogeneity, combined with the tremendous variety of pos-sible excited and ground states dynamics, exploring multi-dimensional intertwined potential energy surfaces, confers to molecular strong coupling a potential that remains to be fully understood. In the next section, we will elaborate on different theoretical approaches, aiming at a first understanding of the light-molecules strong coupling regime.

1.2.2 The molecular strong coupling regime

Following the path of typical cQED experiments, we would like to investigate the new eigen-states that the system might develop when immersed in a structured electromagnetic vac-uum. To simplify the discussion, we will focus on the case of molecules embedded in a Fabry-Pérot (FP) cavity, however the main results derived here will remain valid for any kind of electromagnetic resonator, provided that the light-matter coupling strength and the resonator losses remain in the same ratio. In particular, the strong coupling to plasmonic resonators will reveal as a versatile tool as we will see in the last chapter of this thesis. We will start by describing the optical response of the resonator when filled with molecular absorbers using classical linear response theory before introducing a quantum mechanical description of the coupled systems dynamics. The abstraction of the system to two coupled levels will give us insights in the nature of the new light-matter eigen-states, while its extension to more complex situations will provide a more realistic guideline to understand experimental results.

Despite its completely classical character, linear response theory remains a very accurate tool at describing the modal structure of many quantum systems. This fact should not be too surprising given that one can always cast a linear response function that will effectively describe the (quantum

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mechan-1.2 light-molecules strong coupling 18

ical) microscopic response of the system to a weak external probe. This weak perturbation response is precisely what one is looking for when investigating the modal structure of a system either quantum or classical. The linear response function will obviously not be an accurate tool to describe the dynamics of the system when non-linearities emerge or when quantum statistics become important.

The mode structure of a FP cavity is ruled by the interfer-ence between multiple scattering of light on the cavity mirrors. The condition for constructive interference thus defines the resonant cavity modes where the electromagnetic field builds up, while the field amplitude is strongly reduced elsewhere:

φ =2Lωn/c + 2φr=2mπ (m∈N), (1.2)

where φ is the round trip phase accumulation in the cavity of length L, n is the real part of the refractive index of the intra-cavity medium, ω is the vacuum frequency of light, φr

is the reflection phase from the cavity mirrors, and m labels the order of the cavity modes. We show in Fig. 1.3(a) the calculated round-trip phase accumulation for a 140 nm thick FP cavity with 35 nm thick Ag mirrors, together with its simulated transmission spectrum using transfer matrix methods (TMM). As can be seen, a Lorentzian resonance develops at the energy where the round-trip phase accumulation corresponds to an integer times 2π, with a quality factor Q ' 20 as set by the Ag mirrors.

When such a cavity is filled with a highly absorbing molecular layer, the refractive index of the intra-cavity medium becomes strongly dispersive close to the peak of absorption owing to Kramers-Kronig relations [60]. This dispersive line shape contributes directly to the round-trip phase accumula-tion, allowing multiple solutions to the resonance condition (1.2) for a given cavity mode order. As shown in Fig.1.3(b), for a sufficiently strong absorbing medium, i.e. a sufficiently disper-sive refractive index, three distinct solutions to the resonance condition develop, with the concomitant emergence of a split

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Figure 1.3 – (a) Transfer matrix simulation of the transmission spectrum of a 140 nm thick FP cavity with 35 nm thick Ag mirrors. A resonant mode appears every times the round-trip phase accumulation (cyan curve) matches an integer times 2π (horizontal black lines). (b) Cavity transmission spectra (blue curves) for an increasingly strong embedded absorber (green to red curves). The corresponding round-trip phase accumula-tion funcaccumula-tions (bottom panel) show multiple crossings with a given mode order for sufficiently strong absorption.

doublet in the cavity transmission spectrum. The absence of the central solution from the cavity transmission spectrum is due to the strong dissipation occurring at this energy, preventing the mode to build up.

From this modal approach, it is then straightforward to derive the temporal response of the system, subjected to a pulsed probe field. For a femto-second (fs) incident probe field having a Fourier limited frequency content large enough to cover the two transmission peaks of the spectrum of Fig.1.3(b), the time dependent transmitted intensity displays damped oscillations, as shown in Fig.1.4(b), with a period τ given by

τ =2π/ΩR, (1.3)

where ΩR is the frequency splitting between the cavity modes,

and an attenuation constant that depends on the finesse of the bare resonator and on the absorption losses at the new peaks positions.

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Figure 1.4– (a,b) Simulation of the time dependent transmission of the cavity of Fig.1.3(b) for an increasingly strong absorber. The incident fs pulse is shown in black. For clarity, the panel (a) shows absorbance ranging from 0.01 to 0.13, and panel (b) from 0.15 to 1. The corresponding transmission (green to orange curves) and absorption spectra (black curves) are shown in (c) and (d).

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Thus, we naturally recover from the linear response theory the two hallmarks of the strong light-matter coupling regime: eigen-states splitting and ringing temporal dynamics. The strong light-matter coupling condition stated in section1.1can thus be recast in the linear dispersion theory as follow: the dispersive line-shape of the refractive index must give solutions to the FP equation (1.2) that are separated by more than the full width at half maximum (FWHM) of the absorption line shape (avoiding strong absorption losses) and more than the cavity FWHM (sustaining at least one ringing oscillation) [61].

Remarkably, at the onset of strong coupling (between panels (a) and (b) of Fig. 1.4), their exist a regime where even though the transmission spectrum shows a clear splitting (e.g. orange curve of panel (a)), the corresponding splitting in the absorption spectrum is not well resolved, while in the time domain the dynamical behavior of the system displays over-damped oscillations. This intermediate coupling regime corresponds to a non-perturbative, non-ringing regime that has been discussed in both atomic [62] and semiconductor physics [63, 64]. It results that the actual strong coupling (ringing) regime requires the observation of a resolved splitting in absorption, not only in transmission or in reflection as it will be quantitatively discussed below.

An interesting consequence of this linear dispersion model is that the total polariton relaxation rate depends both on the photon escape rate γ and on the damping at the frequency of the polariton modes ρ(ω0±ΩR)due to the tails of absorption of the

active layer, a quantity that can significantly vary depending on the material under study. This polariton drag could potentially be suppressed by selectively bleaching an inhomogeneously broadened active layer at the polariton frequencies, hence lead-ing to an increased coherence time in the system as proposed by Krimer and coworkers [65].

In order to see how ringing dynamics can emerge at a microscopic level, we now turn to a quantum mechanical description of the light-molecules coupled system. We will start with a very basic Hamiltonian approach to the problem,

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idealizing the molecular medium to an assembly of N two-level systems (e.g. purely electronic transitions), and modeling the cavity by a single quantized mode. We will then discuss some recent developments that significantly improve this model to describe more realistic light-molecule strongly coupled sys-tems.

1.2.3 A two-level systems approach: the Jaynes-Cummings model

Let us start by considering the following Hamiltonian describing the dipolar coupling of a charge q to the electric field of an optical mode [2]:

Hdip_{= −q}_{R · E(0),}

(1.4) withR the position operator of the coupled charge and E(0) is the electric field operator taken at the position of the charge. In the second quantization formalism, the electric field operator at a point ~r of the considered optical mode (ωc,~kc, ~c)is mapped

onto a quantized harmonic operator: E(~r) =ı ζ. ₀h~cf(~r)ae . ı~kc·~r₋_~ c∗f∗(~r)a†e− . ı~kc·~ri_, _(1.5)

where ζ0 is a normalization factor, f is a dimensionless scalar

function describing the spatial structure of the cavity mode of polarization ~c and wave-vector ~kc, and a†(a) is the usual

bosonic ladder operator populating (depleting) the photonic field. The relationship between the mode frequency ωcand its

wave-vector ~kc is fixed by a dispersion relation ω(~kc) that we

will derive below for the specific case of a FP cavity. Setting the electromagnetic field energy of a state with n photons to be equal to ωc(n +1/2), we obtain the following normalization

condition:

hn| Z

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where the zero-photon energy ωc/2 corresponds to the

zero-point motion of the field operator. From this constrain we can express the factor ζ0 as:

ζ₀= r

ωc

20V, (1.7)

with the effective mode volume V defined as: V =

Z |f(r)|2

d3r. (1.8)

It should be noted that, while this definition of the mode volume is formally correct, it diverges for realistic cavity designs. In particular, it has been generalized to treat lossy cavities in the quasi-mode formalism [66]. For planar FP cavities, the lateral mode extension is set by the photon in-plan diffusion length, a quantity in turn related to the cavity mirrors losses.

We now express the dipole moment operator D = qR in terms of spin-flip operators σ+,−. A 1/2−spin immersed

into a fictive magnetic field will be our toy model for matter, considered as a two level system at this stage. Assuming that the fictive magnetic field is aligned with a chosen spin quantization axis, the two eigenstates of this system are the usual up|0i and down|1i states with respective eigenenergies +1 and −1. In this framework, the transition between two different energy states |gi and |ei of the absorber corresponds to the spin-flip |1i → |0i. In the Fock state representation, D is purely non-diagonal as it corresponds to transitions between the available energetic states. ExpandingD along the spin-flip matrices we obtain:

D = d( ~aσ−+~a∗σ+), (1.9)

where ~a is the polarization of the transition and d is the

corresponding dipole matrix element:

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The dipolar coupling Hamiltonian now reads: Hdip_{= −d [}_~ aσ−+~a∗σ+]· . ı ζ₀h~cf(0)a − ~c∗f∗(0)a† i . (1.11) Setting f(0) = 1 at the position of the absorber, we can expend the scalar product and obtain:

Hdip = −ı. Ω0 2 h aσ+− a†σ− i −ı dζ. ₀h~a· ~caσ−−~a∗· ~c∗a†σ+ i , (1.12) where the coupling constant Ω0/2 is defined as:

Ω0/2 = dζ0~a· ~c∗= d r ωc 20V ~ a· ~c∗. (1.13)

Ω₀ is termed the vacuum Rabi frequency. The first part of the coupling Hamiltonian (1.12) describes the emission/absorption of light by a two level system. The second part accounts for processes in which, either the absorber emits and one photon is absorbed, or the absorber gets excited while one photon is emitted. For near resonant light-matter interaction, those latter terms beat at high frequencies in the rotating frame and can thus be neglected as long as Ω0 remains a small fraction of

ωc [2]. However, if Ω0 approaches ωc, these counter-rotating

terms become important, leading to a qualitatively new regime, termed the ultra-strong coupling regime, where phenomena such as ground-state squeezing, band-gap opening, and dynam-ical Casimir effect appear [67–71]. We will explore some aspects of this regime in the context of strong coupling of light with molecular vibrations in chapter 3.

The total light-matter Hamiltonian in the rotating-wave approximation (RWA) is known as the Jaynes-Cummings model [23]: HJC= ωeg(σ+σ−−I/2) + ωc a†a +I/2 −ı. Ω0 2 h aσ+− a†σ− i , (1.14)

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with ωeg the energy of the optical transition of the absorber.

This model has been extended by Tavis and Cummings to N in-dependent absorbers immersed in the same cavity mode, show-ing that its main features remained qualitatively unchanged upon replacing the absorber operator by collective bosonic excitation (Dicke) operators [34] and replacing the individual coupling frequency Ω0 by a collective Rabi frequency:

ΩR= Ω0

√

N. (1.15)

This extension thus results in the appearance of collectivity in the ensemble of absorbers, and the concomittant enhancement of the light-matter coupling strength by a factor that depends on the number of absorbers in the optical mode volume,i.e. the concentration of the active medium.

The Jaynes-Cummings Hamiltonian (1.14) can be directly diagonalized in the single excitation manifold via the Hopfield-Bogoliubov procedure [72], yielding eigen-states that are linear combinations of optical and material excitations: the polari-tonic states

|P+_{i = cos(θ/2)}_|e,0i+_ı.

sin(θ/2)|g,1i |P−

i = sin(θ/2)|e,0i−ı. cos(θ/2)|g,1i,

(1.16) (1.17) where the mixing angle θ is defined as tan(θ) = ΩR/∆, with

∆ = ωeg− ωc the detuning parameter. This very fundamental

model of an absorber immersed in the vacuum fluctuations of an optical mode thus directly gives rise to maximally entangled excited states, separated by the Rabi frequency Ω0(or ΩRin the

Nabsorbers case).

Another key feature of hybrid light-matter states that triggered a huge interest stems from their peculiar dispersion relation. In the specific case of a planar FP cavity, translational invariance allows us to label the different polaritonic states

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Figure 1.5 – (a) Energy dispersion of the polaritonic states as obtained from (1.14). The uncoupled absorber and photonic modes are shown in black dashed lines, yielding resonant coupling at k// = 0. (b) Photonic Hopfield coefficient of the

lower (red) and upper (blue) polaritonic states. At resonance, the two polaritonic states have equal optical and material character.

according to the conserved in-plan momentum of their photonic component k//. The energy dispersion of the FP cavity mode:

ωc(k//) = c nc k~kk = c nc r mπ L 2 + k2_//, (1.18) with c the celerity of light, nc the background refractive

in-dex, m the cavity mode order and L the cavity thickness, here translates into a k//-dependent detuning. The polaritonic

dispersion, obtained by diagonalizing (1.14) at different k//,

shows an energy minimum at k//=0, and a parabolic behavior

in its vicinity (see e.g. Fig. 1.5). This polariton trap in momentum space, associated with the low transverse mass of the light-matter eigenstates:

m∗_//= d

2

dk2_//ωc(k//) !−1

, (1.19)

down to∼ 10−4 times the effective mass of an exciton in a solid, is at the heart of the studies on polariton BEC.

In the time domain, the dynamical evolution of an opened system subjected to the Hamiltonian (1.14) and to Markovian material and optical losses can be described using a quantum trajectories algorithm. As shown in Fig. 1.6(a, blue histogram),

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the relaxation dynamics of an initial photon population toward the optical reservoir of states (photon escaping the cavity) shows an exponential decay when the light-matter coupling strength is smaller that the relaxation rates. In this weak coupling regime, the relaxation is already modified with respect to that of an empty cavity (dashed curve) as some of the initial photon population ends up in the absorber reservoir (green histogram). This effect is reminiscent of donor-acceptor energy transfer dynamics, as we will discuss further in chapter 2. When the light-matter coupling strength overcomes the losses, Fig. 1.6(b), the system enters the strong coupling regime with a typical damped Rabi oscillatory behavior similar to that of Fig. 1.4(b). The clear quadrature between the photon and the absorber reservoirs directly reveals the periodic energy exchange between the two coupled systems. This transition from weak to strong coupling can be quantified by looking at the eigen-solutions of (1.14) when the uncoupled modes frequencies are complex. In this case, the diagonalization yield complex polariton energies whose real parts are separated by a frequency splitting: ∆ω = r |ΩR|2− κ 2− γ 2 2 (1.20) Thus the ringing regime of strong coupling, i.e ∆ω being real, results from the condition |ΩR|2 > (κ₂ − γ₂)2. However, as

dis-cussed in the previous section from a spectroscopic view point, the distinguishability of the two new polaritonic eigenstates as a criterion of strong coupling implies the more restrictive condition [63]: |ΩR|2 > κ

2_+γ2

2 . In other words, the polariton

splitting (twice the interaction frequency) must be larger than the average FWHM of the uncoupled modes. Despite those technical considerations, it can be seen from the decay dynam-ics in the non-pertubative no-ringing regime that profound modifications of the light-matter system can already occur at moderated coupling strength.

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Figure 1.6 – 104 Quantum trajectory simulations of time evolution under the Jaynes-Cummings Hamiltonian 1.14 at resonance, in the presence of photon relaxation (at a rate γ/2) and absorber relaxation (at a rate κ/2), for weak (a) and strong (b) coupling regimes. The blue (green) histogram corresponds to the arrival time of excitation in the photonic (absorber) bath. The black dashed line is an exponential decay function of time constant (2/κ + 2/γ).

We will complete this chapter by briefly exposing some more advanced models, aiming at understanding the strong coupling of a optical mode to complex molecular media.

1.2.4 More complex models: toward cavity quantum chemistry

A first extension of the Tavis-Cummings model to solid state systems was proposed by Houdré and coworkers [73], by accounting for the energetic disorder usually present in an ensemble of absorbers. There, it was shown that the Rabi splitting in such systems remained proportional the square root of the number of absorbers N, while the two polaritonic states were retaining their homogeneous linewidth ((γ + κ)/2). In this situation, the (N − 1) remaining states form linear combinations of purely material excitations with no mixing to the photonic mode, and thus constitute a pool of dark states, bounded to the energy span of the bare absorbers. Also not optically active, such states can have a profound impact on the dynamics of strongly coupled systems as they can be reached by internal relaxation of the polaritonic states. Moreover, it should be noted that despite their purely material character, they remain

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nevertheless coherent superpositions [74], potentially linking together remote absorbers, something that is often a hurdle to achieve in material science [75,76].

The first extension of this model toward the description of molecular strong coupling was proposed Agranovich and coworkers in 1997 [37] where they showed that organic and inorganic excitons could collectively participate in polaritonic states, allowing a versatile tuning of their character as a func-tion of detuning. In a series of following papers [77–81], striking differences between organic and inorganic polaritons were pointed out, in particular due to the localized nature of organic materials excitons (so-called Frenkel excitons) and to their high level of disorder (energetic, positional and orienta-tional). As a result of this translational symmetry breaking, the dispersion relation of strongly coupled disordered materials was shown to consists in both polariton states of well defined wave vector and other hybrid light-matter states for which the wave vector is not a ’good quantum number’. Moreover, these theoretical studies predicted the existence of a large number of uncoupled excitonic states where the excitations would accumulate before relaxing toward coherent polaritonic states, either via spontaneous emission in the coupled cavity mode structure or via non-radiative processes such as the emis-sion of intramolecular phonons. By using a thermodynamical approach to this two-populations problem, Canaguier-Durand and coworkers [82] could determine a fractions of coupled molecules exceeding 60% in ultra-strongly coupled molecular systems.

In 2009, La Rocca and coworkers proposed a toy model to describe such intracavity polariton pumping [83, 84]. In their model, the effect of vibronic progressions present in typical organic materials was mimicked by including 4 electronic levels: two in the excited state manifold and two in the ground-state manifold. Including coherent coupling for the high oscillator strength transitions and scattering processes among the other energy levels, they could show numerically that the lower polaritonic branch could be strongly populated by resonant

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phononic scattering from an exciton reservoir. This prediction was shortly followed by the first demonstration of organic polariton lasing in mono-crystalline anthracene, directly ex-ploiting this resonant scattering mechanism [40]. This model is currently being extended, in a fully fermionic basis, to the case of two coherently coupled molecular ensembles in order to describe recently reported results on polariton energy transfer phenomenon [85–87].

In these extensions of strong coupling physics to molec-ular materials, a common feature is the fact that scattering rates are defined between coupled and uncoupled excitonic states. As pointed out by Canaguier-Durand and coworkers [88], suchad-hoc scattering terms naturally emerge when considering non-Markovian effects in the polariton dynamics. Indeed, with Rabi frequencies approaching optical transitions frequencies, the finite memory time of the vibronic bath prevents one from imparting bare material relaxation rates to the polaritons through a mere change of basis. Instead, the polariton relax-ation rates have to be related to the uncoupled ones through integral equations [89–92], or can be directly defined on the dressed states diagram leading to genuine polaritonic scatter-ing rates. Non-Markovian environment dynamics can lead to counter-intuitive results such as unbalanced lifetimes for the upper and lower polaritons, eventually exceeding both the bare molecule and the empty cavity photon lifetimes, as shown in the next chapter.

In order to better realize the implications of light-mater strong coupling in complex molecular systems, one however has to go beyond a purely vibronic states description of the material. This approach recently appeared in the field of density func-tional theory (DFT), where Tokatly and Rubioet al. successfully combinedab initio quantum mechanical calculations and cavity QED concepts [93,94]. This new approach laid the ground for an accurate description of molecular strong coupling and for an understanding of the accumulating experimental results on new material and chemical properties under strong coupling [46]. Among the blossoming extensions of this approach over the last

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two years [95–105], the redefinition of the Born-Oppenheimer surfaces and the profound modifications of conical intersections between potential energy surfaces appear to be key players in the observed and predicted properties of complex chemical matter under (ultra-)strong light-matter interaction.

Hence, given the current state of theoretical understand-ing of molecular strong couplunderstand-ing, some of the results pre-sented in this thesis will only be discussed within the polariton basis, building up a self-consistent description of these new light-matter states and of the possibilities that they can offer. This way of reasoning remains so-far the only approach to understand e.g. modified chemical reactions under strong coupling [14, 15], where both the complex molecular land-scape and the non-Markovian dynamics dictate the observed behavior. Whenever the studied phenomenon will only rely on a few well identified degrees of freedom, we will try to trace its description to the uncoupled basis and to develop toy models mimicking its behavior, thus providing insights into the physics at play. A general description of molecular polaritonic systems thus remains elusive so far, the underlying challenges being somewhat similar to those currently faced in the field of quantum biology, with the understanding of coherent and entangled dynamics near conical intersections of molecular potential energy surfaces.

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2

D Y N A M I C S A N D E N E R G Y F L O W I N S T R O N G LY C O U P L E D M O L E C U L E S

In this chapter, we investigate different aspects of popu-lation dynamics and energy pathways in molecular ensembles strongly coupled to a cavity mode. The first section summa-rizes a photophysical study of a typical organic material used for light-molecules strong coupling: J-aggregates of TDBC. In particular, we report on the fluorescence quantum yield of its polariton emission and on its transient dynamics, as a function of the Rabi splitting. This is achieved by precisely tuning the TDBC layer position within the optical mode of a Fabry-Pérot (FP) microcavity. This section is followed by a comparative study of polariton photophysics in three archetypal molecular species, illustrating how chemical diversity can translate into rich polaritonic behavior.

Building upon this study of polariton dynamics, we demon-strate in the third section the possibility of transferring en-ergy through hybrid light-matter states in which two different molecular species participate collectively. The efficiency of this new energy transfer mechanism is shown to be independent of the distance separating the energy donor and the energy acceptor molecules. To understand these results, we develop two different models, one based on a cavity modified Forster mechanism, and the other relying on a quantum trajectories algorithm.

This chapter is completed by an investigation of the non-linear response of polaritonic states. In particular, we report on their remarkable efficiency for second harmonic generation.

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2.1 fluorescence quantum yield and transient dynamics 33

2.1 f l u o r e s c e n c e q u a n t u m y i e l d a n d t r a n s i e n t d

y-n a m i c s

Throughout this chapter we will study strongly coupled organic materials embedded into low finesse planar metallic FP cavities (F ' 30). Such cavities, despite their poor photon storage time (ca. 50 fs), provide the very small mode volumes required to achieve large Rabi splittings, as discussed in the previous chapter. This can be illustrated by filling such a cavity with a polymer matrix doped with a high load of J-aggregates of TDBC cyanine dyes (0.1 mol/L, intermolecular distance of ca. 3 nm), having a J-band absorption peak at 588 nm. The resulting cavity transmission spectrum, shown in Fig. 2.1(c), clearly reveals the formation of two polaritonic states, separated in energy by a Rabi splitting of 325 meV, amounting to 15% of the J-band frequency. Such a large energy gap opening should impact the dynamical evolution of the system, and thus consitutes a case study of how collective strong coupling could modify molecular photophysical properties. Moreover, as a direct consequence of the dipolar coupling of molecules to the cavity mode, this Rabi splitting can be tuned by accurately positioning the molecules within the mode profile as we now demonstrate. Parts of this section are reproduced from already published work [106].

2.1.1 Spatial tuning of strong coupling in FP cavities

2.1.1.1 Experimental methods

We developed a bonding technique for the precise control of the position of a molecular layers in a FP cavity. First, a 30 nm thick silver film was sputtered on a glass substrate, forming the first cavity mirror. A dielectric layer of poly(methyl methacrylate) (PMMA) was then was spin-coated on top, form-ing a spacer of tunable thickness (referred to as ’slab A’). Meanwhile, another 30 nm thick silver mirror was deposited on a flexible 1 mm thick poly-(dimethylsiloxane) (PDMS)

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sub-2.1 fluorescence quantum yield and transient dynamics 34

Figure 2.1 – (a) Energy level representation of the coupling of a molecular transition (J0− J1) to an optical resonance forming

the hybrid states P+ and P− separated in energy by the Rabi splitting ( hΩR). (b) Absorption (red curve) and emission

spectrum (blue dashed curve) of a layer of J-aggregate TDBC. (c) Schematic illustration of TDBC dispersed in a first mode FP cavity everywhere. Transmission spectrum of the empty cavity (red dashed curve) and of the cavity filled with polymer doped TDBC (back curve), giving rise to P+ and P-. Figure reproduced from reference [106].

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strate by thermal evaporation. This mirror was also coated with a layer of PMMA of chosen thickness (labeled ’slab B’). The surface of the PMMA spacer of slab A was made hy-drophilic by spin-coating a 2 nm thick PDMS layer on it from a 0.3 wt% PDMS solution in tert-butanol and exposing it to an oxygen plasma for 30 s. Next, alternated layers of TDBC J-aggregates (1,1’-diethyl-3,3’-bis(4-sulfobutyl)-5,5’,6,6’-tetra-chlorobenzimidazolocarbocyanine, inner salt, sodium salt, few Chemicals) and of the polycation poly-(diallyldimethyl-ammonium chloride) (PDDA, average molecular weight 200000− 350000, 20 wt% in water, Aldrich) were adsorbed onto the sur-face via layer-by-layer (LBL) assembly [107,108]. Polyelectrolyte layers were adsorbed by soaking slab A for 5 min in a solution of PDDA (6 × 10−2 M in deionized water), and J-aggregate layers were deposited by soaking it for 5 min in a solution of TDBC (1 × 10−4M in deionized water) which was previously sonicated for 60 min at 35 °C. In order to reach the high absorption coef-ficient necessary for strong coupling, we repeated this bi-layers deposition process 10 times, thus forming a thin (ca. 25 nm) active layer absorbing close to 70% of the incident light at the maximum of the J-band. The surface of slab B was coated with a 2 nm thick film of PDMS. Finally, the polymer face of slab B was sealed to the molecular film surface of slab A to form the optical microcavity, as represented in Fig. 2.2. By controlling the thickness of the PMMA layers on slab A and slab B, the position of the J-aggregate layers could be moved from the edge of the cavity to its center with nanometric precision. The whole cavity length, including the PMMA and molecular films, could be tuned such that the J-aggregates absorption band at 588 nm was resonant with one of the optical modes of the FP cavity. The thickness of each layer was measured using an Alpha-step IQ surface profilometer.

2.1.1.2 Results and discussion

We show in Fig. 2.3 the transmission spectra of first and second mode cavities as the active layer is moved from the

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Figure 2.2 – Scheme of the layer-by-layer tunable microcavity. Figure reproduced from reference [106].

edge to the center. In the case of a first mode cavity, the Rabi splitting increases from 310 meV when the layer is close to the edge to 500 meV when it is positioned at the field antinode. In this configuration, the splitting increases by 60% over that obtained when the cavity is homogeneously filled with a layer of TDBC having the same absorption coefficient as the LBL assembly. Performing the same position tuning in a second mode cavity, we observe the transition from strong to weak coupling regime as the active layer reaches the central node of the cavity. Such position dependence of the Rabi splitting within the cavity mode are accurately reproduced by transfer matrix calculations, as shown in Fig. 2.3(c, f). Moreover, the reduction of the Rabi splitting in going from a first to a second mode cavity is consistent with the increase in the cavity mode volume (see Eq. (1.13)):

Ωλ/2_R Ωλ_R ∝ s Vλ Vλ/2 ' 1.6, (2.1)

as estimated from transfer matrix calculations, with λ/2 and λ indices denoting the first and second mode cavities respectively.

The strong coupling to the cavity mode is further evi-denced by measuring angle dependent transmission spectra, as

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Figure 2.3 – Spectroscopy of the first (top row) and second mode (bottom row) cavities. (a,d) Schematic representation of the cavities and their calculated field amplitudes (real part of the electric field obtained by propagating a resonant monochromatic plan wave from the left side of the structure). (b,e) Transmission spectra of a set of cavities resonantly tuned to the TDBC J-band. The molecular layer is located at different positions inside the cavity (z from the edge to the center as indicated by the dashed blue arrow). The consecutive spectra are offset by 18% for clarity. The spectra were measured under 35o incident transverse electric polarized light. (c,f) Rabi splittings as a function of the LBL TDBC position inside the cavity mode (blue dashed line in (c) represents the splitting obtained when the molecules are dispersed evenly inside the cavity). The purple dashed line in (f) indicates the FWHM of the cavity mode (150 meV). Black dots in (c) and (f) are the calculated splittings using transfer matrix simulation where the complex refractive index of the TDBC J-aggregate film was extracted from its absorption spectrum via a Kramers-Kronig transformation and the thickness of the Ag mirrors and PMMA spacer layers were taken from experiments. Figure reproduced from reference [106].

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Figure 2.4 – Angular-dependent transmission spectra of a first mode cavity embedding the LBL TDBC layer at the mirror edge (a) and in the center (b) of the cavity. The angle of transverse electric polarized incident light was varied from 0oto 65o. The black dot-dashed curves and white dashed curves represent respectively the dispersion of the empty cavity mode and that of the bare TDBC J-band. Figure reproduced from reference [106].

exemplified for two different cavities in Fig. 2.4, where a clear anticrossing about the bare TDBC J-band is observed.

To go beyond these modal properties and investigate the excited states dynamics we first studied the photo-luminescence (PL) emission spectra of the LBL TDBC cavities upon off reso-nant monochromatic excitation (520 nm, filtered xenon lamp). We compare in Fig. 2.5 the normal incidence PL spectra of first and second mode cavities with the active layer placed at the nodes and anti-nodes of the field. A first striking observation from those spectral line shapes is that the upper polariton mode (expected atca. 550 nm) does not emit. Instead, we obtain double peaked PL spectra where one contribution appears near the lower polariton state energy and the other at the bare J-band energy. Clearly, several mechanisms beyond the Tavis-Cummings model are at play here.

First, the absence of PL from the upper polariton state is reminiscent of what is observed in many aromatic molecules, where only the lower excited state emits, an effect known as Kasha’s rule. This is due to the fact that higher molecular excited states are often lying within the vibronic manifolds of lower excited states. At room temperature, such non-radiative

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Figure 2.5– Fluorescence emission spectra collected normal to the sample plan (0.1 collection and excitation numerical aperture, 520 nm excitation wavelength). (a) First mode cavity with the TDBC molecular layer placed at the edge (z = 2 nm, black curve) and at the center (z = 62 nm, red curve) of the cavity. (b) Second mode cavity with the layer placed at the edge (z = 2 nm, black curve), at the first antinode of the field (z = 62 nm, red curve) and at the center of the cavity (z = 162 nm, blue curve). Figure reproduced from reference [106].

decay pathways usually dominates the excited states dynamics, channeling the energy to the lowest energy excited state from which PL can eventually occur. As discussed above, the descrip-tion of the vibronic structure of organic polariton systems is not trivial. However, the absence of upper polariton emission is a clear evidence of complex energy pathways within strongly coupled molecular systems. It should also be noted that upper polariton emission has been reported in low temperature exper-iments [109], further evidencing the role of vibrational modes in the polariton relaxation dynamics.

The presence of an emission peak at the J-band position in the spectra of Fig. 2.5 clearly shows that, even though all molecules are located at equivalent positions in the cavity mode volume, two different populations coexist: a strongly coupled one and an uncoupled one. In our system, this could be due to orientational and solvation disorder in the J-aggregates ensemble. As mentioned in the first chapter, the existence of un-coupled states and their impact on the polariton dynamics has been the subject of many theoretical [77–82] and experimental

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works [110–113] as it is of fundamental importance for possible applications of strongly coupled systems.

In view of those observations, a clear advantage of our LBL cavity design is that the system can be continuously tuned from a mostly polaritonic emission (Fig. 2.5(b), red curve) to a completely uncoupled emission (Fig.2.5(b), blue curve). Using this system, we now investigate in details the fluorescence quantum yield of the lower polaritonic state upon off-resonant excitation, thus obtaining key information on the polariton relaxation pathways.

2.1.2 PL quantum yield and transient dynamics

2.1.2.1 Experimental methods

The fluorescence quantum yield of the strongly coupled system was measured relative to a standard [114]. This ap-proach amounts to comparing the emission over absorption ratio of the sample to that of a reference of known absolute quantum yield Φr: Φs= Φr Is fs(λex) fr(λex) Ir n2_s(λem) n2 r(λem) , (2.2)

where I refers to the integrated emission intensity, f(λex) is

the fraction of light absorbed at the pumping wavelength (λex),

n(λem) is the background refractive index of the medium at

the emission wavelength (λem), and the indices (r, s) denote

the reference and sample respectively. Our protocol consists in three steps. First, we measured the absolute quantum yield of a standard dye using a commercial integrating sphere setup (Hamamatsu C11347-11). This value was then used as a ref-erence for computing the quantum yield of a thin polymer film (PMMA) containing the same standard dye. Finally, we obtained the quantum yield of strongly coupled TDBC by comparison to this new reference quantum yield. This calibration technique allows one to go in a controlled way from the measurements of dilute solutions to that of solid thin film samples.

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The reference dye molecule (Lumogen F Red 300, LR) dissolved in spectroscopic grade chloroform was chosen for the overlap of both its absorption and emission spectra with that of the strongly coupled TDBC cavities, thus ensuring no wavelength sensitivity issues in the estimations of fs(r) and

I_s(r) . Another important advantage of this LR dye is its very low sensitivity to environmental conditions. In particular, we measured a constant fluorescence lifetime of (5.8 ± 0.05) ns in dilute chloroform solutions after bubbling Ar for 10 minutes, indicating the absence of oxygen quenching. The same lifetime was also measured from the doped PMMA thin film, also constant upon successive degassing under Ar. The absorbance of the solution and of the thin film of LR was kept below 0.1 at maximum to limit fluorescence re-absorption effects. The absorption spectra were measured using a Shimadzu UV3101 spectrometer and the emission spectra were acquired on an Horiba Fluorolog-3 fluorimeter. The results are reported in Fig.2.6(a,b).

The fluorescence quantum yield of coupled and uncou-pled TDBC samples were measured under off-resonant excita-tion at 520 nm, and under resonant excitaexcita-tion of the upper polariton state at 550 nm. The results were the same in the two cases, in agreement with the Kasha rule stated above. The effect of the finite numerical aperture of collection on the measurement of the dispersive polariton emission band was corrected by an angle resolved analysis (see Fig.2.6(c)).

2.1.2.2 Results and discussion

The fluorescence quantum yield is a direct measure of the relative importance of radiative relaxation pathways in the excited state dynamics, and can be expressed (in agreement with (2.2)) as

Φf=

kr

kr+ knr

= τ· kr, (2.3)

where krand knrare the radiative and nonradiative decay rates

and τ is the lifetime of the emitting state. For a bare TDBC film outside the cavity, we measured a PL quantum yield of 0.02 by